2. Contents
β’ The mean for grouped frequency table.
β’ The range and modal class for grouped frequency table.
β’ The median for grouped frequency table.
3. Mean for grouped frequency table
To find mean for grouped frequency table, need to multiply frequency by midpoint then sum of
products divide by sum of frequency.
Example: In Tim's school, there are 25 teachers. Each teacher travels to school every morning in his or
her own car. The distribution of the driving times (in minutes) from home to school for the teachers is
shown in the table below:
The driving times are given for all 25 teachers, so the data is for a population. Calculate the mean of the driving
times.
Driving Times (minutes) Number of Teachers
0 to less than 10 3
10 to less than 20 10
20 to less than 30 6
30 to less than 40 4
40 to less than 50 2
4. Mean for grouped frequency table
Solution: Step 1. Determine the midpoint for each interval.
β’ For 0 to less than 10, the midpoint is 5.
β’ For 10 to less than 20, the midpoint is 15.
β’ For 20 to less than 30, the midpoint is 25.
β’ For 30 to less than 40, the midpoint is 35.
β’ For 40 to less than 50, the midpoint is 45.
Step 2: Multiply each midpoint by the frequency for the class.
β’ For 0 to less than 10, 5 Γ 3 = 15.
β’ For 10 to less than 20, 15 Γ 10 = 150.
β’ For 20 to less than 30, 25 Γ 6 = 150.
β’ For 30 to less than 40, 35 Γ 4 = 140.
β’ For 40 to less than 50, 45 Γ 2 = 90.
5. Mean for grouped frequency table
Step 3: Add the results from Step 2 and divide the sum by 25.
15 + 150 + 150 + 140 + 90 = 545
π =
545
25
= 21.8
Each teacher spends a mean time of 21.8 minutes driving from home to school each morning.
To better represent the problem and its solution, a table can be drawn as follows:
Driving
Times (minutes)
Number
of Teachers π
Midpoint
Of Class π
Product ππ
0 to less than 10 3 5 15
10 to less than 20 10 15 150
20 to less than 30 6 25 150
30 to less than 40 4 35 140
40 to less than 50 2 45 90
6. Example
β’ The ages of 100 singers of a 360-member choir are shown in the table below: Calculate the mean of the ages.
Answer: 42.7 years.
Ages of Members (years) Number of Members
20 to less than 25 12
25 to less than 30 14
30 to less than 35 10
35 to less than 40 8
40 to less than 45 20
45 to less than 50 6
50 to less than 55 5
55 to less than 60 4
60 to less than 65 11
65 to less than 70 10
7. Example
β’ The following table shows the weights of children in a class. Using this information estimate the mean weight.
Answer: 48.6 kg.
